correlated noise model
pmelchior opened this issue · comments
When we fit HSC + HST data, the noise model is incorrect because the pixels are correlated in HST coadds. In essence, we’re overfitting the HST data.
We could kill the correlation by whitening the noise, but that introduces extra noise. The best option is to modify the log likelihood function of Observation
with a proper multivariate Gaussian with a given covariance matrix. The problem is: that matrix is large, and to good approximation banded. But autograd
(or jax
) don’t support sparse matrices (yet). The computation is identical to convolution with our apply_filter
method, which we have already put into the autodiff path. So I suggest that we create a subclass CorrelatedObservation
, where we overwrite the constructor with one that replaced weights
by covariance
, and that reimplements get_log_likelihood
and log_norm
for proper correlated signals.